The embodiments of the invention generally relate to a circuit simulation that creates synthetic single finger data using a scaled simulation and extracts a single finger model from the synthetic single finger data and a random dopant fluctuation (RDF) model.
When characterizing small area field effect transistors FETs for modeling, it is common practice to measure an ensemble of many devices in parallel and then use the average current as the typical behavior of a single small device. [1] This reduces the sampling error caused by random dopant fluctuation and line edge roughness. However, using this average current introduces a distortion of the drain current versus gate voltage characteristics. Specifically in the subthreshold and low overdrive regions the average current in the ensemble is higher than the typical current, but in the high overdrive region the average current equals the typical current. This application presents a compact modeling method for accurate extraction of typical behavior from ensemble measurements and reproducing either single finger or ensemble currents for circuit simulation.
Consider a small FET composed of two fingers. In the absence of manufacturing variations each finger has the same current voltage (IV) characteristics and the current of the two fingers in parallel is twice the current of one finger. In practice small FET fingers display variation in threshold voltage due to random dopant fluctuations (RDF).[2] Suppose the threshold voltage of one finger in our hypothetical FET is 30 millivolts higher than typical and that of the other finger is 30 millivolts lower. On average the fingers have the typical Vt and so in some sense this is a typical FET subject to RDF. One finger will have more current than typical and the other less. Well above threshold, the differences in current from typical will be roughly proportional to the differences of threshold voltage Vt from typical because the current is roughly linear with gate voltage. In this example, the total current will be approximately twice the typical value for one finger. On the other hand, below threshold, the current is exponentially related to the threshold voltage and the two fingers will not have equal and opposite current deltas. If one finger has twice the typical current and the other will have roughly half the typical current. The total current will be 2.5 times the typical for one finger, not two times as we might expect from a typical device.
If the Vt of the total device is measured by the single point method a lower Vt than the average of the individual finger Vt's will be found. This effect has been observed when trying to estimate the quiescent current for CMOS SRAMs [3] and logic chips [4,5]. These researchers have noted that the distribution of off currents is lognormal because of the logarithmic relationship between off current and both threshold voltage and FET gate length.
This effect must be considered when extracting a compact model from measurements of multiple devices in parallel. If the model is adjusted to match line targets it is important to understand the structures used to establish and monitor the line targets. Ensemble devices will produce higher off current targets and lower Vt targets than single finger devices for the same manufacturing process. Finally since circuit designers use small FETs both in parallel arrangements and as single FETs, the compact model needs to be able to model both cases correctly.
These and other aspects of the embodiments of the invention will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following descriptions, while indicating preferred embodiments of the invention and numerous specific details thereof, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the embodiments of the invention without departing from the spirit thereof, and the embodiments of the invention include all such modifications.